The finite element analysis of elasto-plastic materials by use of dislocation dipole systems

It is shown how the stress field due to any prescribed continuous distribution of dislocation dipoles can be determined. This technique then forms the basis of a general method of solution of elasto-plastic material problems. The presentation is limited to situations which conform to either plane stress or strain conditions. Some results are obtained for relatively simple geometrical and loading configurations and compared with classical plasticity solutions. Finally, the method is applied to the problem of a circular hole in a finite strip under tension.     

铝包带包裹高压输电线路导线的微动损伤

在自制的微动试验装置上对铝包带包裹钢芯铝绞导线（ACSR）进行微动试验研究。振幅1．0mm,2．0×107次微动循环后,研究内、外层铝股线及钢芯线的磨损状况,测定其抗拉强度,探讨铝包带包裹导线的微动损伤机制。结果表明：外层铝股线表面经受铝包带的刮擦以及磨粒磨损;内层铝股线微动磨损斑呈椭圆形,部分磨损斑下有疲劳裂纹;而钢芯线的损伤微弱,仅发生镀锌层的磨损、脱落。铝包带对导线有较好的保护作用,内外层铝股线的抗拉强度均高于未包裹导线的抗拉强度。     

输电线钢芯铝绞线精密压接成形的有限元分析

目的 针对钢芯铝绞线在压接过程中出现断裂的现象,对其压接工艺进行探究,优化现有压接工艺,制定更精密的压接方法,防止断裂缺陷的产生.方法 利用ABAQUS有限元模拟软件,以弹塑性变形理论为基础,采用等效摩擦力的方法建立有限元压接模型,通过实验验证模型的精确性,并计算在不同压接长度、压接次数下钢芯铝绞线的塑性变形量.结果 ...     

A drafting program for isoparametric finite elements

Considerable effort has been invested lately in the application of isoparametric finite elements for numerical solution of a wide range of applied mechanics problems. In fact, several general purpose computer programs are now available which are based upon such finite elements. In the present paper, a new application of the isoparametric finite element concept is introduced which significantly extends its usefulness for many practical structural configurations. In this application, final working or architectural drawings of the structure are made from the same (or similar) finite element model as was utilized in a structural integrity analysis. The hardware necessary to produce such drawing, a computer driven plotter or automated drafting machine, is available commercially or through most data centres, and the software concepts required are described herein.     

Adaptive finite element computation of dielectric and mechanical intensity factors in piezoelectrics with impermeable cracks

The paper deals with the application of an adaptive, hierarchic‐iterative finite element technique to solve two‐dimensional electromechanical boundary value problems with impermeable cracks in piezoelectric plates. In order to compute the dielectric and mechanical intensity factors, the interaction integral technique is used. The iterative finite element solver takes advantage of a sequence of solutions on hierarchic discretizations. Based on an a posteriori error estimation, the finite element mesh is locally refined or coarsened in each step. Two crack configurations are investigated in an infinite piezoelectric plate: A finite straight crack and a finite kinked crack. Fast convergence of the numerical intensity factors to the corresponding analytical solution is exemplarily proved during successive adaptive steps for the first configuration. Similar tendency can be observed for the second configuration. Furthermore, the computed intensity factors for the kinks are found to coincide well with the corresponding analytical values. In order to simulate the kinks spreading from a straight crack, the finite element mesh is modified automatically with a specially developed algorithm. This forms the basis for a fully adaptive simulation of crack propagation. Copyright © 2009 John Wiley & Sons, Ltd.     

On the relationship between the finite element and finite difference methods

The integral equations which arise from application of the Galerkin-finite element scheme to the convective diffusion equation are examined to illustrate how this method represents differential equations. The formulae obtained are effectively spatial averages of standard finite difference equations written at a node. The truncation error in the finite element solution at a node is obtained for various nodal configurations.     

NMLMAP-A two dimensional finite element program for transient or static, linear or nonlinear magnetic field problems

NMLMAP is a finite element program for the solution of two dimensional magnetic field problems. The problems may be transient or static, linear or nonlinear, and planar or axisymmetric. The program has features that include a coarse-to-fine rezone technique; an adaptive acceleration method for speeding the convergence of the nonlinear iteration; and a substructuring technique for decreasing solution times in certain non-linear problems. These features, the governing and finite element equations, and example problems are discussed     

Harmonic enrichment functions: A unified treatment of multiple,intersecting and branched cracks in the extended finite element method

A unifying procedure to numerically compute enrichment functions for elastic fracture problems with the extended finite element method is presented. Within each element that is intersected by a crack, the enrichment function for the crack is obtained via the solution of the Laplace equation with Dirichlet and vanishing Neumann boundary conditions. A single algorithm emanates for the enrichment field for multiple cracks as well as intersecting and branched cracks, without recourse to special cases, which provides flexibility over the existing approaches in which each case is treated separately. Numerical integration is rendered to be simple—there is no need for partitioning of the finite elements into conforming subdivisions for the integration of discontinuous or weakly singular kernels. Stress intensity factor computations for different crack configurations are presented to demonstrate the accuracy and versatility of the proposed technique. Copyright © 2010 John Wiley & Sons, Ltd.     

Analysis of the voltage harmonic distortion at buses feeding office loads

The harmonic distortion of the phase-to-neutral voltage at low-voltage buses feeding office load is investigated for various cable configurations, lengths and cross-sections. The investigation is carried out with a software model that was validated with analytical expressions and measurements taken at a real installation. It is shown that the selection of a cable should be based not only on its ampacity and allowable voltage drop but also on its configuration, in order to avoid excessive voltage harmonic distortion. Configurations where the neutral conductor is part of a four-core cable lead to relatively small harmonic distortion, whereas cable configurations where the neutral conductor runs separately cause high-voltage harmonic distortion. In the latter case, the neutral conductor develops a significant voltage with respect to the ground. Increasing the cross-section of the neutral conductor, as the existing standards dictate, may prevent its overloading from zero-sequence harmonic currents but hardly improves the voltage harmonic distortion at the load bus.     

Effective mechanical properties of EM composite conductors: an analytical and finite element modeling approach

An analytical model and numerical approach to predict the effective mechanical properties of a composite conductor consisting of metallic core and insulation layers are presented in this paper. The analytical model was developed based on a two-step homogenizations and mechanics analysis for composite unit cell. The Step 1 homogenization derives the effective properties of the out-wrapped composite insulation layers. The Step 2 homogenization further smears the metallic core and the effective composite insulation layers to develop homogenized mechanical properties for composite conductor according to appropriate homogenization sequences. The procedure of using numerical approach and finite element method to determine the unit cell effective constants were also described and the results of the FEA prediction were presented. The analytical predictions were compared well to the numerical results for the nine material constants that characterize the effective mechanical properties of the composite conductor.     

Refined h-adaptive finite element procedure for large deformation geotechnical problems

Adaptive finite element procedures automatically refine, coarsen, or relocate elements in a finite element mesh to obtain a solution with a specified accuracy. Although a significant amount of research has been devoted to adaptive finite element analysis, this method has not been widely applied to nonlinear geotechnical problems due to their complexity. In this paper, the h-adaptive finite element technique is employed to solve some complex geotechnical problems involving material nonlinearity and large deformations. The key components of h-adaptivity including robust mesh generation algorithms, error estimators and remapping procedures are discussed. This paper includes a brief literature review as well as formulation and implementation details of the h-adaptive technique. Finally, the method is used to solve some classical geotechnical problems and results are provided to illustrate the performance of the method.     

2-D multiplane finite element technique for solving a class of 3-D problems

A finite element technique, for efficient solution of a class of 3-D elasticity problems, is presented. In this method, standard 2-D finite elements are used along with a ‘connector’ element. An element, previously used to model material interfaces, is shown to provide the properties for use as a ‘connector’ element, if input variables are redefined. The accuracy of the technique is illustrated with a sample solution.     

A multiplicative finite strain finite element framework for the modelling of semicrystalline polymers and polycarbonates

This paper presents a phenomenological model for the simulation and analysis of stress‐induced orientational hardening in semicrystalline polymers and polycarbonates at finite strains. The notion of intermediate (local) stress‐free configuration is used to develop a set of constitutive equations, and its relation to the multiple natural (stress‐free) configurations in the class of materials being considered here is discussed. A hyperelastic stored energy function, written with respect to the intermediate stress‐free configuration is presented to model the finite elastic response. It is then combined with the J₂‐flow theory to model the finite inelastic response. The isochoric constraint during inelastic deformation is treated via an exact multiplicative decomposition of the deformation gradient into volume‐preserving and spherical parts. The numerical solution algorithm is based on the use of operator splitting technique that results in a product formula algorithm with elastic‐predictor/inelastic‐corrector components. Numerical results are presented to show the behaviour of the model. Copyright © 2000 John Wiley & Sons, Ltd.     

Autonomous decentralized finite element method and its applications

In this paper, a new solution procedure using the finite element technique in order to solve problems of structure analysis is proposed. This procedure is called the autonomous decentralized finite element method because it is based on the characteristic autonomy and decentralization in life or biological systems (life‐like approach). The fundamental approach is developed according to an idea of cellular automata manipulation by the new neighbourhood model. The finite element method with an algorithm of the relaxation method is adopted as the solution procedure in this approach. The proposed procedure demonstrates that it is a powerful means of numerical analysis for many kinds of structural problems that are structural morphogenesis, structural optimization and structural inverse problems. Our procedure is applied to numerical analysis of three simple plane models: (1) The structural shape analysis problem for the prescribed displacement mode of a truss structure, (2) An adaptive structure remodelling problem on an elastic continuum, (3) An identification problem of thermal conductivity on a continuum. The effectiveness and validity of our idea are shown from their numerical results. Copyright © 2003 John Wiley & Sons, Ltd.     

高压架空钢绞Al导线的腐蚀与防护

钢绞Al导线（Aluminium Conductor Steel Reinforced,ACSR）是我国高压输电线路主要的导体材料。在工业污染或沿海区,ACSR导线发生较严重腐蚀,导致强度降低,甚至断线,影响输电安全,提高运行成本。本文基于Al及Zn的溶液及大气腐蚀腐蚀机理,综述了国内外有关ACSR导线的腐蚀机理、影响腐蚀的因素、腐蚀对ACSR导线性能的影响及ACSR导线的防护的研究成果,并就今后如何在实验室内开展工业污染环境下的ACSR导线腐蚀研究提出自己的观点。     

On the rotation of conductors of finite torsional stiffness by eccentric snow loading and control of rotation using counterweights

This paper is concerned with the prevention of snow loading on an overhead conductor caused by the mechanism of cylindrical-sleeve growth. The eccentric snow loading on the windward side of the conductor, having finite torsional stiffness, causes the conductor to rotate and a theoretical study of how this rotation can be controlled on attaching counterweights along the span of the conductor is presented. In the absence of counterweights, the non-linear rotation equation is solved analytically in terms of elliptic functions, simulating ice loading by a uniform torque density; for large torque density an asymptotic solution is obtained using matched asymptotic expansions. In the rotation equation the counterweights producing torque at discrete points are incorporated as delta functions which enable the discontinuity in the twisting couple at such locations to be accounted for by means of an integral moment balance. A simple algorithm is then presented for integrating the equation of rotation as an initial value problem which can deal with any distribution of counterweights along the span of the conductor. Illustrative numerical results are presented for zero, one, two, three and four counterweights per span; in the absence of counterweights analytical and numerical solutions are in exact agreement.     

分裂导线舞动非线性有限元分析方法

采用具有三个平动自由度和一个扭转自由度的三节点等参单元离散覆冰导线,用欧拉梁单元离散间隔棒,考虑覆冰导线所受空气动力的非线性和导线大幅运动的几何非线性,利用虚功原理建立覆冰分裂导线非线性有限元方程。用Newmark时间积分和Newton-Raphson非线性迭代法求解有限元方程。编制了相应的计算程序,通过算例验证了方法和程序的正确性。进一步利用由风洞实验获得的覆冰四分裂导线的空气动力系数,模拟研究具有不同档距的覆冰四分裂线路的舞动,为舞动防止技术的研究提供参考。所给出的方法适用于任意多分裂导线的舞动研究。     

Failure analysis of aluminum cable steel reinforced (ACSR) conductor of the transmission line crossing the Paraná River

The failure of the conductor of the 460 kV overhead transmission line located along the crossing of the Paraná River was investigated. As a result of this failure, a blackout took place in the southern states of Brazil in January of 2002, reaching approximately 67 million inhabitants. Investigation of the external aluminium layer of the ACSR conductor near the fracture showed typical static deformation marks and dynamic fretting wear tangential marks, both associated with the presence of Al₂O₃ debris. Additionally, encrusted silicon particles were observed on the external surface of the strands. The internal Al layer showed elliptical deformation marks also associated with Al₂O₃ debris. Both Al₂O₃ and Si particles are efficient abrasive material, which associated with slight relative motion of metallic surfaces (clamp/strand and strand/strand) can promote fretting wear. Two types of fracture surface of the Al strands were identified: 45° and quasi-normal surfaces, the former being the predominant type. Delamination and particle detachment were the mechanisms of superficial degradation observed on the Al strands, indicating that the rupture of the strands occurred under a gross slip fretting regime induced by sub-conductor oscillation. Inspection of the internal surface of as-cast Al–10%Si spacer clamps revealed different stages of intense circumferential wear caused by the preferential cracking and particle detachment of the eutectic constituent of the as-cast microstructure. This intense wear reduces the clamping contact pressure, which allows higher displacement amplitude and leads to the critical fretting regime. Finally, a few suggestions are discussed to minimise the occurrence of future failures.     

A consistent finite element technique for recovery of distributed reactions and surface tractions

An effective technique is presented for recovering surface tractions and distributed reaction forces from finite element displacement solutions of structural mechanics problems. Nodal values of surface tractions and assumed trial functions are used to represent the distribution of surface stresses. Equations obtained from the familiar Galerkin formulation are used to compute the nodal traction values. The method is demonstrated to be efficient and highly accurate, even in the presence of jump conditions or singularities. Extensions of the method are possible for recovering secondary solution variables in non-structural finite element applications.     

The finite difference technique for solving crack problems

A detailed examination of the Finite Difference method for solving crack problems is presented and discussed. The three classical mode I configurations (i.e. Centered Crack Plate, Double Edge Notch and Single Edge Notch) as well as an uncommon case (A Penny Shape Crack embedded in a circular plate in bending) are solved and discussed. The Stress Intensity Factors are computed by taking more than one (first) term in William's Series, using two or three points near the tip. This technique improves the accuracy and frees one from relying on the very first point near the tip as a measure base. In most cases, the accuracy was found to be between 1–3% for uniform mesh size in the order of 5% from the half crack length. No special imposed functions were used near the tip, which makes the technique competitive to the Finite Element method, especially for 3-D problems or cases where the degree of singularity is not known. The solution is found iteratively (a two step SOR method) and some techniques for quick convergence are discussed.